16 hours ago
- Consensus is fundamentally based on simple majority voting, but can get stuck with split votes (e.g., two red, two blue, one green).
- To resolve split votes, a leader is designated to choose a color while others approve, though the leader may be unavailable.
- The solution involves multiple concurrent votes with rotating leaders across a 2D board of columns, where each column operates independently.
- A board is invalid if different columns achieve majorities for different colors; the safety condition requires that any two columns with majorities agree on the same color.
- Players must choose colors that don't conflict with columns to the left, ensuring consistency by assuming fair play and committing majorities to abstain in earlier columns.
- The final decision rule is to pick the rightmost possible color, as other participants' past choices guarantee conflicts have been resolved through prior abstentions.